DES encryption chains these 33 operations on 64-bit quantities:
$$\mathsf{IP}\,,\,g_1\,,\,S\,,\,g_2\,,\,S\,,\,\ldots\,,\,S\,,\,g_{15}\,,\,S\,,\,g_{16}\,,\,\mathsf{IP}^{-1}$$$$\mathsf{IP}\,,\,g_1\,,\,\mathsf S\,,\,g_2\,,\,\mathsf S\,,\,\ldots\,,\,\mathsf S\,,\,g_{15}\,,\,\mathsf S\,,\,g_{16}\,,\,\mathsf{IP}^{-1}$$
where $S$$\mathsf S$ is the "swap" involution defined by $S(L\mathbin\|R)=R\mathbin\|L$$\mathsf S(L\mathbin\|R)=R\mathbin\|L$, function $\mathsf{IP}$ is some permutation of bits, and $\mathsf{IP}^{-1}$ is the inverse permutation.
DES decryption chains these 33 operations on 64-bit quantities:
$$\mathsf{IP}\,,\,g_{16}\,,\,S\,,\,g_{15}\,,\,S\,,\,\ldots\,,\,S\,,\,g_2\,,\,S\,,\,g_1\,,\,\mathsf{IP}^{-1}$$$$\mathsf{IP}\,,\,g_{16}\,,\,\mathsf S\,,\,g_{15}\,,\,\mathsf S\,,\,\ldots\,,\,\mathsf S\,,\,g_2\,,\,\mathsf S\,,\,g_1\,,\,\mathsf{IP}^{-1}$$
- For $j=33$, because $\mathsf{IP}$ cancels $\mathsf{IP}^{-1}$.
- For $j=1$, because $\mathsf{IP}^{-1}$ cancels $\mathsf{IP}$.
- For other even $j$, because $g_{j/2}$ is an involution.
- For other (odd) $j$, because $S$$\mathsf S$ is an involution.
The usual definition of a round of a Feistel cipher includes the swap $S$$\mathsf S$:
$$\begin{align}
g'_n(L\mathbin\|R)&=S\bigl(g_n(L\mathbin\|R)\bigr)\\
&=R\mathbin\|\bigl(L\oplus f(R,K_n)\bigr)
\end{align}$$$$\begin{align}
g'_n(L\mathbin\|R)&=\mathsf S\bigl(g_n(L\mathbin\|R)\bigr)\\
&=R\mathbin\|\bigl(L\oplus f(R,K_n)\bigr)
\end{align}$$
and this function is not its own inverse per the sense in the question.
With that notation, DES encryption and decryption are the 18 operations
$$\mathsf{IP}\,,\,g'_1\,,\,g'_2\,,\,\ldots\,,\,g'_{15}\,,\,g_{16}\,,\,\mathsf{IP}^{-1}\\
\mathsf{IP}\,,\,g'_{16}\,,\,g'_{15}\,,\,\ldots\,,\,g'_2\,,\,g_1\,,\,\mathsf{IP}^{-1}$$
In that presentation, it is less apparent that decryption undoes encryption. But that still holds, and becomes obvious again if we expand the $g'_n$ into $g_n$ followed by $S$$\mathsf S$.
Footnote per comment: There is always some form of swap between rounds of a Feistel cipher, so that the fraction of the state that did not change in a round changes onin the next round. That's essential for security (not for decryption to work). A round is its own inverse only if we do notexclude include the swap as part of its definition, as most authors do.
